Prove that `|z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2` is purely imaginary.

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

Prove that |z_1+z_2|^2=|z_1|^2, ifz_1//z_2 is purely imaginary.

Prove that |z_1+ z_2|^2= |z_1|^2+ |z_2|^2 if and only if (z_1/z_2) is purely imaginary.

Prove that |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2),quad if z_(1)/z_(2) is purely imaginary.

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z1^2-z2^2|=| z 1^2+ z 2 ^2-2( z )_1( z )_2| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z_1^2-z_2^2|=| z_ 1^2+ z _2 ^2-2( z _1)( z _2)| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z_1^2-z_2^2|=| z_ 1^2+ z _2 ^2-2( z _1)( z _2)| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2